Special Radical Research Articles

Generalization of primary ideal associated with a special radical class

Generalization of primary ideal associated with a special radical class

On weakly radical ideals of non-commutative rings

For a commutative ring [Formula: see text] denote the Jacobson radical of the ring by [Formula: see text]. Khashan et al. introduced and studied J-ideals and weakly J-ideals for commutative rings with identity. In this paper, let [Formula: see text] be a non-commutative ring. We introduce weakly [Formula: see text]-ideals for a special radical [Formula: see text] and show that if [Formula: see text] is the Jacobson radical many of the results proved by Khashan et al. are also satisfied for non-commutative rings. The results for weakly J-ideals for non-commutative rings follow as special cases of a more general situation.

On radical ideals of non-commutative rings

Let [Formula: see text] denote the Jacobson radical of a commutative ring [Formula: see text]. In [H. A. Khashan and A. B. Bani-Ata, [Formula: see text]-ideals of commutative rings, Int. Electron. J. Algebra 29 (2021) 148–164], the notion of J-ideals was introduced. If [Formula: see text] denotes the prime radical of a commutative ring then in [U. Tekir, S. Koc and K. H. Oral, [Formula: see text]-Ideals of commutative rings, Filomat 31(10) (2017) 2933–2941], the notion of an [Formula: see text] ideal of a commutative ring was introduced and studied. In this note, we show that these results are special cases of a more general situation. We define [Formula: see text]-ideals for a special radical [Formula: see text] and prove that most of the results of the above-mentioned papers are satisfied for non-commutative rings as a special case.

Theoretical substantiation of the program of special physical training of high school students at the educational level "master"

A preliminary analysis of the physical training of cadets of higher military educational institutions showed that training programs for military professionals in physical education, special physical training need radical changes. This is due to the participation of the Armed Forces of Ukraine in hostilities - the model and practicality of approaches to hostilities have changed dramatically, the conditions of preparation for them require the introduction of military-applied sports in the training process of military professionals. The professional activity of servicemen is accompanied by maximum physical and mental loads in terms of volume and intensity, complexity and variety of tasks in the conditions of lack of time and information, constant risk and threat to life.
 The current program of training future military professionals at the "master's" level to some extent does not meet these requirements for the formation of psychophysical readiness of future officers. This was shown by the participation in the joint forces operation (anti-terrorist operation) in eastern Ukraine, a large number of wounded and killed servicemen during the fighting. Foreign and domestic experts who assessed the conflict came to the conclusion that the servicemen of the Armed Forces of Ukraine were not ready to use weapons in the Republic of Crimea, Donetsk and Luhansk regions during the first stage of the armed conflict.

SPECIAL RADICALS FOR NEAR-RING


 
 
 The concept of a special radical for near-rings has been treated in several nonequivalent, but related, ways in the recent literature. We use the version due to K. Kaarli to establish that various prime radicals and the nil radical are special radicals on the class A of all near-rings which satisfy an extended version of the Andrunakievich Lemma. Since A includes all d.g. near-rings—and much more—these results significantly extend results previously obtained by Kaarli and by Groenewald. We also obtain special radical results for the Jacobson type radicals 30 and 3 1 , albeit on less extensive classes. Examples are given which illustrate and delimit the theory developed. 
 
 

Grafting of zwitterion polymer on polyamide nanofiltration membranes via surface-initiated RAFT polymerization with improved antifouling properties as a new strategy

Special radical grafting strategies, e.g. surface-initiated reversible addition-fragmentation chain transfer (SI-RAFT) polymerization, are considered as promising techniques for the purpose of not only uniformly modifying nanofiltration (NF) membranes with the functional polymers but also preventing nonspecific protein adsorption. In this research work, we decide to report for the first time an efficient approach to stabilize RAFT initiators on the surface of polyamide NF membranes and study the effect of the chain length of the polymer on the membrane fouling performance. For this purpose, using interfacial polymerization between trimesoyl chloride (TMC) and a mixture of diamines (i.e. 1,3-phenylenediamine (MPD) and (3,5-diamino phenyl) methanol (DAPM), polyamide thin film composite NF membranes were synthesized. Afterward, the reaction between the polyamide thin film composite layer and α-bromoisobutyryl bromide (BIBB) was carried out. It was found that the stabilized amount of BIBB on the surface of the prepared membranes could be efficiently enhanced by using the DAPM treatment. Finally, using RAFT polymerization technique, a zwitterionic polymer, poly[(2-methacryloyloxy)ethyl]dimethyl[3-sulfopropyl]ammonium hydroxide (pMEDSAH), was successfully grafted on the membrane surface. It is noteworthy that the irreversible adsorption amount of proteins on the prepared pMEDSAH-grafted membrane appreciably decreased to >96%. All the provided results indicate that all the pMEDSAH-grafted membranes, which were prepared using a facile and efficient method, have proved promising for practical applications.

Weakly Special Classes of Modules

In the development of Theory Radical of Rings, there are two kinds of radical constructions. The first radical construction is the lower radical construction and the second one is the upper radical construction. In fact, the class π of all prime rings forms a special class and the upper radical class of forms a radical class which is called the prime radical. An upper radical class which is generated by a special class of rings is called a special radical class. On the other hand, we also have the class of all semiprime rings which is weakly special class of rings. Moreover, we can construct a special class of modules by using a given special class of rings. This condition motivates the existence of the question how to construct weakly special class modules by using a given weakly special class of rings. This research is a qualitative research. The results of this research are derived from fundamental axioms and properties of radical class of rings especially on special and weakly special radical classes. In this paper, we introduce the notion of a weakly special class of modules, a generalization of the notion on a special class of modules based on the definition of semiprime modules. Furthermore, some properties and examples of weakly special classes of modules are given. The main results of this work are the definition of a weakly special class of modules and their properties.

On polynomial equation rings and radicals

The notion of n-polynomial equation ring, for an arbitrary but fixed positive integer n, is introduced. A ring A is called an n- polynomial equation ring if γ(A[Xn ]) = γ(A)[ Xn ], for all radicals γ. If this equation holds for all hereditary radicals γ, then A is said to be a hereditary n-polynomial equation ring. Various characterizations of these rings are provided. It is shown that, for any ring A, the zero-ring on the additive group of A is an n- polynomial equation ring and that any Baer radical ring is a hereditary n- polynomial equation ring. New radicals based on these notions are introduced, one of which is a special radical with a polynomially extensible semisimple class.

Pseudomyxoma peritonei induced by low-grade appendiceal mucinous neoplasm accompanied by rectal cancer: a case report and literature review

BackgroundPseudomyxoma peritonei (PMP) is a disease involving the peritoneum characterized by the production of large quantities of mucinous ascites. PMP has a low incidence, is difficult to diagnose, and has a guarded prognosis. PMP induced by low-grade appendiceal mucinous neoplasm is extremely rare, and PMP accompanied by rectal cancer is even rarer.Case presentationWe present a unique case of a 70-year-old male with PMP induced by low-grade appendiceal mucinous neoplasm accompanied by rectal cancer. The patient’s clinical, surgical, and histologic data were reviewed. The patient had persistent distended abdominal pain without radiating lower back pain, abdominal distension for 1 month, and no exhaustion or defecation for 4 days. A transabdominal ultrasound-guided biopsy was performed on the first day. The patient received an emergency exploratory laparotomy because of increased abdominal pressure. We performed cytoreductive surgery, enterolysis, intestinal decompression, special tumour treatment and radical resection of rectal carcinoma. The postoperative course was uneventful. The postoperative histological diagnoses were PMP, low-grade appendiceal mucinous neoplasm and rectal medium differentiated adenocarcinoma. At the 1-year follow-up visit, no tumour recurrence was observed by computed tomography (CT). We also performed a literature review.ConclusionsWe should be aware that PMP can rarely be accompanied by rectal cancer, which represents an easily missed diagnosis and increases the difficulty of diagnosis and treatment. Additionally, there are some typical characteristics of PMP with respect to diagnosis and treatment.

A PRIME ESSENTIAL RING THAT GENERATES A SPECIAL ATOM

A special atom (respectively, supernilpotent atom) is a minimal element of the lattice $\mathbb{S}$ of all special radicals (respectively, a minimal element of the lattice $\mathbb{K}$ of all supernilpotent radicals). A semiprime ring $R$ is called prime essential if every nonzero prime ideal of $R$ has a nonzero intersection with each nonzero two-sided ideal of $R$. We construct a prime essential ring $R$ such that the smallest supernilpotent radical containing $R$ is not a supernilpotent atom but where the smallest special radical containing $R$ is a special atom. This answers a question put by Puczylowski and Roszkowska.

Special Right Jacobson Radicals for Right Near-rings

In this paper three more right Jacobson-type radicals, J r g , are introduced for near-rings which generalize the Jacobson radical of rings, 2 f0;1;2g. It is proved that J r g is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a J r g -semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-g , 2 f0;1;2g. Moreover, a nite right g2-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-eld (which is isomorphic to eRe), where e is a right g2-primitive idempotent in R.

Spectroscopic study on the sonodynamic and sonocatalytic damage of anthraquinone derivants to bovine serum albumin under ultrasonic irradiation

In this work, three anthraquinone derivants (Alizarin: 1,2-dihydroxy-9, 10-anthraquinone, Alizarin–DA: 1,2-dihydroxy-9, 10-anthraquinone-3-aminomethyl-N, N-diacetic acid and Alizarin–DA–Fe: 1,2-dihydroxy-9, 10-anthraquinone-3-aminomethyl-N, N-diacetate-Ferrous(III)) were used to study the sonodynamic and sonocatalytic damage of bovine serum albumin (BSA) molecules according to the hyperchromic effect of UV–vis spectra and quenching effect of intrinsic fluorescence. Meanwhile, some influencing factors such as ultrasonic irradiation time, anthraquinone derivants concentration and ionic strength on the damage of BSA molecules were also considered. The results show that the synergetic effect of anthraquinone derivants and ultrasonic irradiation can efficiently damage the BSA molecules. Finally, some special radical scavengers were used to determine the kind of generated reactive oxygen species (ROS) in the presence of three anthraquinone derivants under ultrasonic irradiation. The results show that the ROS, at least, including singlet oxygen ( 1O 2) and hydroxyl radicals (OH) are generated during the sonodynamic and sonocatalytic processes. It is wished that this paper could offer some valuable references for the application of anthraquinone derivants in sonodynamic therapy (SDT) and sonocatalytic therapy (SCT) for tumor treatment.

Radicals and l-modules

We show that for any special class of l-modules, we can define a special class of l-rings. We prove that the special radical of an l-ring R can be represented as the intersection of the l-annihilators of l-modules over R belonging to the special class. The prime radical of an l-ring R can be represented as the intersection of the l-annihilators of l-prime l-modules over R.

Radicals of l-rings and special classes of l-modules

A special class of lattice-ordered modules is studied. We show that for any special class of l-modules we can define a special class of l-rings. The special radical of an l-ring R can be represented as the intersection of the l-annihilators of l-modules over R belonging to the special class. The prime radical of an l-ring R can be represented as the intersection of the l-annihilators of l-prime l-modules over R.

Special classes of l-rings

We study a special class of lattice-ordered rings and a special radical. We prove that a special radical of an l-ring is equal to the intersection of the right l-prime l-ideals for each of which the following condition holds: the quotient l-ring by the maximal l-ideal contained in a given right l-ideal belongs to the special class. The prime radical of an l-ring is equal to the intersection of the right l-semiprime l-ideals. We introduce the notion of a completely l-prime l-ideal. We prove that N 3(R) is equal to the intersection of the completely l-prime, right l-ideals of an l-ring R, where N 3(R) is the special radical of the l-ring R defined by the class of l-rings without positive divisors of zero.

Special classes of l-rings and Anderson-Divinsky-Sulinski lemma

Special classes of lattice-ordered rings (l-rings) are studied and for special radicals of l-rings the Anderson-Divinsky-Sulinski lemma is proved, i.e., it is proved that if ρ is a special radical in the class of l-rings and I is an l-ideal of an l-ring R, then ρ(I) is an l-ideal of the l-ring R and ρ(I) = ρ(R) ∩ I.

On weakly special radical of semigroups

The coincidence of the special radical of semigroups and the Baer radical is established. The characterization of semisimple semigroups in the sense of the Baer radical is found.

On Jacobson Near-rings and Special Radicals

In this paper, we construct special radicals using class pairs of near-rings. We establish necessary conditions for a class pair to be a special radical class. We then define Jacobson-type near-rings and show that in most cases the class of all near-rings of this type is a special radical class. Subsequently, we investigate the relationship between each Jacobson-type near-ring and the corresponding matrix near-ring.

2P317 光合成反応中心スペシャルペアカチオンラジカルのスピン密度分布に関する理論的研究(光生物学(光合成・視覚と光受容),口頭発表,第45回日本生物物理学会年会)

2P317 光合成反応中心スペシャルペアカチオンラジカルのスピン密度分布に関する理論的研究(光生物学(光合成・視覚と光受容),口頭発表,第45回日本生物物理学会年会)

On rings generating supernilpotent and special atoms

We study prime rings which generate supernilpotent (respectively special) atoms, that is, atoms of the lattice of all supernilpotent (respectively special) radicals. A prime ring A is called a **-ring if the smallest special class containing A is closed under semiprime homomorphic images of A. A semiprime ring A whose every proper homomorphic image is prime radical is called a *-ring. We show that the class of all **-rings strictly contains the class of all *-rings and that the smallest supernilpotent (respectively the smallest special) radical containing a nonzero **-ring is a supernilpotent (respectively special) atom. This generalizes H. France-Jackson's results concerning supernilpotent and special atoms. A big open question in radical theory asks whether the prime radical coincides with the upper radical generated by the essential closure of the class of all *-rings. We ask the similar question concerning **-rings and note that a negative answer to our question implies a negative answer to the big question. We also give some necessary and sufficient conditions for a prime ring to generate a supernilpotent atom which might help to answer the big open question.